You are the workshop manager. Boards, ribbon, and pipes need to be cut into equal pieces. Use fraction division to figure out exactly how many pieces you get — and how much is left over.
The workshop has materials measured in feet, yards, and meters. Every project requires pieces of a specific fractional length. Work through four phases: divide a whole-number board into fraction-sized shelves, divide a fraction of ribbon into smaller pieces, divide a mixed-number pipe into quarter-meter sections, and decide which cut wastes less — then prove your math with a quick-check problem. Finish with a cut-list memo.
A board is a whole number of feet long. Each shelf needs a fraction of a foot. Divide to find how many shelves and how much is left over.
Dividing by (2/3) is the same as multiplying by (3/2). So 8 ÷ (2/3) = 8 × (3/2) = 24/2 = 12 shelves. In general: L ÷ (2/d) = L × d / 2. Check your answer by multiplying: 12 × (2/3) = 8 ✅.
You have a fraction of a yard of ribbon. Each decoration piece needs a smaller fraction of a yard. Divide fraction by fraction to find how many pieces you can cut.
Multiply by the reciprocal: (5/6) ÷ (1/4) = (5/6) × (4/1) = 20/6 = 10/3 ≈ 3.33 pieces. That means 3 full pieces with 1/3 of a piece left over. The leftover is (10 mod 3)/3 = 1/3 of a piece, which is (1/3) × (1/4) = 1/12 of a yard.
A pipe is a mixed number of meters long. You need to cut it into equal pieces of 1/4 meter each. Convert to an improper fraction, then divide.
Convert 3 1/2 to an improper fraction: (3×2+1)/2 = 7/2 meters. Then divide: (7/2) ÷ (1/4) = (7/2) × (4/1) = 28/2 = 14 pieces. Dividing by 1/4 is the same as multiplying by 4!
Two cutting options — compare the leftover amounts to decide which wastes less material, then prove your fraction division with a quick-check problem.
Write a 3–5 sentence cut-list memo to the workshop team. Use your real numbers to show how many pieces each material yields and which cut option wastes less.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Whole ÷ Fraction | Correct shelf count, leftover shown, and multiplication check works | Correct number of shelves | Set up correctly but computation error |
| Fraction ÷ Fraction | Correct piece count, simplified fraction, decimal, and leftover explained | Correct number of pieces | Multiply-by-reciprocal attempted with error |
| Mixed Numbers | Correct conversion and division, full pieces and remainder both shown | Correct number of pipe pieces | Conversion or division step has an error |
| Communication | Memo identifies better cut with justification and all numbers used | Memo compares cuts and uses most numbers | Memo present but missing key comparisons |